Single-machine resource allocation scheduling with due-date assignment, deterioration effect and position-dependent weights

This article considers scheduling problems with resource allocation, deterioration effect and position-dependent weights on a single machine. For two different due-date assignment methods-i.e. common (CON) due-date assignment and slack (SLK) due-date assignment-a bi-criteria analysis is provided wherein the first objective is to minimize the weighted sum of the absolute value in lateness with a common due date (a common flow-allowance), and the second objective is to minimize the weighted sum of resource consumption. Optimality properties and algorithms are proposed to solve three different versions of considering these two criteria.